Decentralized Maximum Likelihood Estimation for Sensor Networks Composed of Nonlinearly Coupled Dynamical Systems

In this paper we propose a decentralized sensor network scheme capable to reach a globally optimum maximum likelihood (ML) estimate through self-synchronization of nonlinearly coupled dynamical systems. Each node of the network is composed of a sensor and a first-order dynamical system initialized with the local measurements. Nearby nodes interact with each other exchanging their state value and the final estimate is associated to the state derivative of each dynamical system. We derive the conditions on the coupling mechanism guaranteeing that, if the network observes one common phenomenon, each node converges to the globally optimal ML estimate. We prove that the synchronized state is globally asymptotically stable if the coupling strength exceeds a given threshold. Acting on a single parameter, the coupling strength, we show how, in the case of nonlinear coupling, the network behavior can switch from a global consensus system to a spatial clustering system. Finally, we show the effect of the network topology on the scalability properties of the network and we validate our theoretical findings with simulation results.Comment: Journal paper accepted on IEEE Transactions on Signal Processin

Harmonic-Copuled Riccati Equations and its Applications in Distributed Filtering

The coupled Riccati equations are cosisted of multiple Riccati-like equations with solutions coupled with each other, which can be applied to depict the properties of more complex systems such as markovian systems or multi-agent systems. This paper manages to formulate and investigate a new kind of coupled Riccati equations, called harmonic-coupled Riccati equations (HCRE), from the matrix iterative law of the consensus on information-based distributed filtering (CIDF) algortihm proposed in [1], where the solutions of the equations are coupled with harmonic means. Firstly, mild conditions of the existence and uniqueness of the solution to HCRE are induced with collective observability and primitiviness of weighting matrix. Then, it is proved that the matrix iterative law of CIDF will converge to the unique solution of the corresponding HCRE, hence can be used to obtain the solution to HCRE. Moreover, through applying the novel theory of HCRE, it is pointed out that the real estimation error covariance of CIDF will also become steady-state and the convergent value is simplified as the solution to a discrete time Lyapunov equation (DLE). Altogether, these new results develop the theory of the coupled Riccati equations, and provide a novel perspective on the performance analysis of CIDF algorithm, which sufficiently reduces the conservativeness of the evaluation techniques in the literature. Finally, the theoretical results are verified with numerical experiments.Comment: 14 pages, 4 figure

Stability Analysis of Integral Delay Systems with Multiple Delays

This note is concerned with stability analysis of integral delay systems with multiple delays. To study this problem, the well-known Jensen inequality is generalized to the case of multiple terms by introducing an individual slack weighting matrix for each term, which can be optimized to reduce the conservatism. With the help of the multiple Jensen inequalities and by developing a novel linearizing technique, two novel Lyapunov functional based approaches are established to obtain sufficient stability conditions expressed by linear matrix inequalities (LMIs). It is shown that these new conditions are always less conservative than the existing ones. Moreover, by the positive operator theory, a single LMI based condition and a spectral radius based condition are obtained based on an existing sufficient stability condition expressed by coupled LMIs. A numerical example illustrates the effectiveness of the proposed approaches.Comment: 14 page

Static output feedback: a survey

This paper reviews the static output feedback problem in the control of linear, time-invariant (LTI) systems. It includes analytical and computational methods and presents in a unified fashion, the knowledge gained in the decades of research into this most important problem

Theory and computation of covariant Lyapunov vectors

Lyapunov exponents are well-known characteristic numbers that describe growth rates of perturbations applied to a trajectory of a dynamical system in different state space directions. Covariant (or characteristic) Lyapunov vectors indicate these directions. Though the concept of these vectors has been known for a long time, they became practically computable only recently due to algorithms suggested by Ginelli et al. [Phys. Rev. Lett. 99, 2007, 130601] and by Wolfe and Samelson [Tellus 59A, 2007, 355]. In view of the great interest in covariant Lyapunov vectors and their wide range of potential applications, in this article we summarize the available information related to Lyapunov vectors and provide a detailed explanation of both the theoretical basics and numerical algorithms. We introduce the notion of adjoint covariant Lyapunov vectors. The angles between these vectors and the original covariant vectors are norm-independent and can be considered as characteristic numbers. Moreover, we present and study in detail an improved approach for computing covariant Lyapunov vectors. Also we describe, how one can test for hyperbolicity of chaotic dynamics without explicitly computing covariant vectors.Comment: 21 pages, 5 figure